Title :
Approximations by Smooth Transitions in Binary Space Partitions
Author :
Lage, Marcos ; Bordignon, Alex ; Petronetto, Fabiano ; Veiga, Álvaro ; Tavares, Geovan ; Lewiner, Thomas ; Lopes, Hélio
Author_Institution :
Dept. de Mat., Pontificia Univ. Catolica do Rio de Janeiro, Rio de Janeiro
Abstract :
This work proposes a simple approximation scheme for discrete data that leads to an infinitely smooth result without global optimization. It combines the flexibility of binary space partitions trees with the statistical robustness of smooth transition regression trees. The construction of the tree is straightforward and easily controllable, using error-driven metrics or external constraints. Moreover, it leads to a concise representation. Applications on synthetic and real data, both scalar and vector-valued demonstrated the effectiveness of this approach.
Keywords :
approximation theory; pattern clustering; regression analysis; trees (mathematics); binary space partition trees; global optimization; smooth transition regression trees; Classification tree analysis; Computer graphics; Data visualization; Error correction; Function approximation; Image processing; Least squares approximation; Regression tree analysis; Robustness; Time series analysis; Binary Space Partitions; Classification and Regression Tree; Smooth Transition Regression Trees;
Conference_Titel :
Computer Graphics and Image Processing, 2008. SIBGRAPI '08. XXI Brazilian Symposium on
Conference_Location :
Campo Grande
Print_ISBN :
978-0-7695-3358-2
DOI :
10.1109/SIBGRAPI.2008.7